Question

Решите неравенство:а) |10х+1|>21;б) |2-6х|<4

Answer 1

Решите неравенство

а) |10х+1|>21

$\left[\begin{array}{ccc} 10x+1 \ \textgreater \ 21\\ 10x+1 \ \textless \ -21\end{array}\right \\ \\ \\ \left[\begin{array}{ccc} 10x \ \textgreater \ 20\\ 10x \ \textless \ -22\end{array}\right \\ \\ \\ \left[\begin{array}{ccc} x \ \textgreater \ 2\\ x \ \textless \ -2,2\end{array}\right$

Ответ: 
$x \ \textless \ -2,2 \ ; \ x \ \textgreater \ 2$


б) |2-6х|<4

$\left \{ {{2-6x \ \textless \ 4} \atop { 2-6x \ \textgreater \ -4 }} \right. \\ \\ \left \{ {{6x \ \textgreater \ -2} \atop { 6x \ \textless \ 6 }} \right. \\ \\ \left \{ {{x \ \textgreater \ - \frac{1}{3} } \atop { x \ \textless \ 1 }} \right.$

Ответ: 
$- \frac{1}{3} \ \textless \ x \ \textless \ 1$